Structure-oriented Filter by Domain Decomposition

Filtering is a general term for the process of decomposing the input data into a complete set of components and selecting a limited part of these components for the output. It is often used to separate noise from signal, whenever signal and noise have distinct distributions among the set of components. The drawback in such cases is the absence of some components of the original data in the filtered data. We introduce a filter process that preserves the full set of components in the output data. First, the data is decomposed in two components: one dominated by noise and the other dominated by signal. Structure-oriented Smoothing is applied to the noise-dominant part, guided by the signal-dominant part. The smoothed noise component is then combined with the signal component to generate the filtered full-component data. Examples with field data show the advantages of this strategy, as well as its flexibility for several other applications.